The distribution of the maximum of a variance gamma process and path-dependent option pricing

Roman Ivanov ()

Finance and Stochastics, 2015, vol. 19, issue 4, 979-993

Abstract: Although numerical procedures often supply a required accuracy, closed-form expressions allow one to escape any accumulation of errors. In this paper, we discuss the possibility of obtaining explicit results for a variance gamma process. We derive the exact distribution of the maximum of the variance gamma process over a finite interval of time and establish the prices of path-dependent options including digital barrier, fixed-strike lookback, and lookback options. The obtained formulas are based on values of hypergeometric functions. Copyright Springer-Verlag Berlin Heidelberg 2015

Keywords: Variance gamma process; Distribution of maximum; Path-dependent options; Exact formula; Hypergeometric function; 60G51; 60G70; 60J75; 33C20; C02; D46; D53; G12 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s00780-015-0277-8

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